By Jon Aaronson, Toshihiro Hamachi, Klaus Schmidt (auth.), Y. Takahashi (eds.)

ISBN-10: 1461303214

ISBN-13: 9781461303213

ISBN-10: 1461379962

ISBN-13: 9781461379966

In 1992 successive symposia have been held in Japan on algorithms, fractals and dynamical structures. the 1st one used to be Hayashibara discussion board '92: overseas Symposium on New Bases for Engineering technology, Algorithms, Dynamics and Fractals held at Fujisaki Institute of Hayashibara Biochemical Laboratories, Inc. in Okayama in the course of November 23-28 within which forty nine mathematicians together with 19 from overseas participated. They comprise either natural and utilized mathematicians of diverse backgrounds and represented eleven coun attempts. The organizing committee consisted of the next family individuals and Mike KEANE from Delft: Masayosi HATA, Shunji ITO, Yuji ITO, Teturo KAMAE (chairman), Hitoshi NAKADA, Satoshi TAKAHASHI, Yoichiro TAKAHASHI, Masaya YAMAGUTI the second used to be held on the learn Institute for Mathematical technological know-how at Kyoto collage from November 30 to December 2 with emphasis on natural mathematical facet during which greater than eighty mathematicians participated. This quantity is a partial checklist of the stimulating alternate of principles and discussions which came about in those symposia.

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B. Katok, Constructions in Ergodic Theory, preprint. [Katzn] 'Yo Katznelson, An Introduction to Harmonic Analysis, Dover Publ. , New York (1967). [Kr] A. Krygin, Examples of ergodic cascades, Math. Notes USSR, 16, (1974), 1180-1186. [Kw-Le-Ru1] J. Kwiatkowski, M. Lemanczyk, D. Rudolph, Weak isomorphisms of measure-preserving diffeomorphisms, Israel J. Math. (1992), 33-64. [Aa1] 49 [Kw-Le-Ru2] ___ , A class of real cocycles having an analytic coboundary modification, preprint. Niederreiter, Uniform Distribution of Sequences, Wiley,(1974).

Krieger, On ergodic flows and isomorphism of factors, Math. Annalen, 223, (1976), 19-70. I. Kubo, Quasi-flows, Nagoya Math. J. 35, (1969). W. Mackey, Ergodic theory and virtual groups, Math. Ann. 166, (1966), 187-207. W. Parry, Compact Abelian groups extensions of discrete dynamical systems Z. Wahrsch. w Geb. 13, (1969), 95-113. [Sch) K. Schmidt, Cocycles of Ergodic Transformation Groups, Lect. Notes in Math. Vol. 1, MacMillan Co. of India (1977). 25 KOKSMA'S INEQUALITY AND GROUP EXTENSIONS OF KRONECKER TRANSFORMATIONS Jon Aaronson l , Mariusz Lemailczyk2, Christian Mauduit3, and Hitoshi Nakada4 lSchool of Mathematical Sciences, Tel Aviv University 69978 Tel Aviv, Israel 2Institute of Mathematics, Nicholas Copernicus University ul.

83, (1961), 573-60l. Sinel'shchikov, Existence and uniqueness of cocycles of an ergodic automorphism with dense ranges in amenable groups, Kharkov preprint, Inst. Low Temp. Phys. & Engin. (1983). Sinel'shchikov, Classification and structure of cocycles of amenable ergodic equivalence relations, Kharkov preprint, Inst. Low Temp. Phys. & Engin. (1993). Hamachi, The normalizer group of an ergodic automorphism of type III and the commutant of an ergodic flow, J. Funct. Anal. 40, (1981), 387-403. Hamachi, A measure theoretical proof of Connes- Woods theorem on ATflows, Pacific J.

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